Start to snigger and make fun of garment (5)
I believe the answer is:
smock
'garment' is the definition.
(I have seen 'Loose garment ' mean 'smock' so perhaps 'garment' could also mean 'smock')
'start to snigger and make fun of' is the wordplay.
'start to' indicates taking the first letters.
'and' means one lot of letters go next to another.
'make fun of' becomes 'mock' (to make fun of someone is to mock or tease them).
The first letter of 'snigger' is 's'.
's'+'mock'='SMOCK'
(Other definitions for smock that I've seen before include "Artist's loose overall" , "Artist's, peasant's, overall" , "Loose dress or blouse" , "artist's attire" , "Loose overall or dress" .)